Solve for $x$ and $y$ using elimination. ${-5x-3y = -29}$ ${2x+3y = 26}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-3x = -3$ $\dfrac{-3x}{{-3}} = \dfrac{-3}{{-3}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-5x-3y = -29}\thinspace$ to find $y$ ${-5}{(1)}{ - 3y = -29}$ $-5-3y = -29$ $-5{+5} - 3y = -29{+5}$ $-3y = -24$ $\dfrac{-3y}{{-3}} = \dfrac{-24}{{-3}}$ ${y = 8}$ You can also plug ${x = 1}$ into $\thinspace {2x+3y = 26}\thinspace$ and get the same answer for $y$ : ${2}{(1)}{ + 3y = 26}$ ${y = 8}$